Biharmonic conformal maps in dimension four and equations of Yamabe-type
Differential Geometry
2017-07-12 v1
Abstract
We prove that the problem of constructing biharmonic conformal maps on a -dimensional Einstein manifold reduces to a Yamabe-type equation. This allows us to construct an infinite family of examples on the Euclidean 4-sphere. In addition, we characterize all solutions on Euclidean 4-space and show that there exists at least one non-constant proper biharmonic conformal map from any closed Einstein 4-manifold of negative Ricci curvature.
Keywords
Cite
@article{arxiv.1707.03326,
title = {Biharmonic conformal maps in dimension four and equations of Yamabe-type},
author = {Paul Baird and Ye-Lin Ou},
journal= {arXiv preprint arXiv:1707.03326},
year = {2017}
}
Comments
15 pages